Ill-Posedness of the Hydrostatic Euler and Singular Vlasov Equations

Daniel Han-Kwan; Toan T. Nguyen

doi:10.1007/s00205-016-0985-z

Ill-Posedness of the Hydrostatic Euler and Singular Vlasov Equations

Daniel Han-Kwan
, Toan T. Nguyen

École Polytechnique

Pennsylvania State University

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we develop an abstract framework to establish ill-posedness, in the sense of Hadamard, for some nonlocal PDEs displaying unbounded unstable spectra. We apply this to prove the ill-posedness for the hydrostatic Euler equations as well as for the kinetic incompressible Euler equations and the Vlasov–Dirac–Benney system.

Original language	English
Pages (from-to)	1317-1344
Number of pages	28
Journal	Archive for Rational Mechanics and Analysis
Volume	221
Issue number	3
DOIs	https://doi.org/10.1007/s00205-016-0985-z
Publication status	Published - 1 Sept 2016

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title = "Ill-Posedness of the Hydrostatic Euler and Singular Vlasov Equations",

abstract = "In this paper, we develop an abstract framework to establish ill-posedness, in the sense of Hadamard, for some nonlocal PDEs displaying unbounded unstable spectra. We apply this to prove the ill-posedness for the hydrostatic Euler equations as well as for the kinetic incompressible Euler equations and the Vlasov–Dirac–Benney system.",

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AU - Nguyen, Toan T.

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N2 - In this paper, we develop an abstract framework to establish ill-posedness, in the sense of Hadamard, for some nonlocal PDEs displaying unbounded unstable spectra. We apply this to prove the ill-posedness for the hydrostatic Euler equations as well as for the kinetic incompressible Euler equations and the Vlasov–Dirac–Benney system.

AB - In this paper, we develop an abstract framework to establish ill-posedness, in the sense of Hadamard, for some nonlocal PDEs displaying unbounded unstable spectra. We apply this to prove the ill-posedness for the hydrostatic Euler equations as well as for the kinetic incompressible Euler equations and the Vlasov–Dirac–Benney system.

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U2 - 10.1007/s00205-016-0985-z

DO - 10.1007/s00205-016-0985-z

M3 - Article

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EP - 1344

JO - Archive for Rational Mechanics and Analysis

JF - Archive for Rational Mechanics and Analysis

IS - 3

ER -

Ill-Posedness of the Hydrostatic Euler and Singular Vlasov Equations

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